PRESSURE is increasing on Opposition Leader Tony Abbott to broaden his promised investigation into the Australian Workers Union affair, with two Liberal MPs urging a general inquiry into union behaviour and governance.

Shadow parliamentary secretary Jamie Briggs, who advised former prime minister John Howard on industrial relations, said there seemed to be a ''cultural problem'' in parts of the union movement.

He said such a broad inquiry should include looking at industry superannuation funds about which allegations had been made.

Tony Abbott. Photo: Craig Abraham

Mr Briggs said all options should be kept open on the form of the inquiry.

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After Mr Abbott last week promised a Coalition government would order the probe into the AWU slush fund affair, former Liberal workplace minister Peter Reith urged that it be made more general, and also pointed to the importance of probing industry superannuation funds.

Former union leader and one-time New South Wales Labor treasurer Michael Costa has said the Gillard government should order a judicial inquiry into the management of unions.

Victorian Liberal backbencher Dan Tehan urged an inquiry into union governance in an address to the HR Nicholls Society on Monday night.

''Tony Abbott has called for a judicial review into the allegations of a slush fund in the AWU, but equally there is scope for this to go further and to examine other rorts, such as those discovered in the HSU,'' Mr Tehan said.

Such a review could also consider whether industry associations and unions should have higher standards of corporate governance, using the changes being proposed under Coalition policy as a starting point, he said.

Mr Abbott has put forward a private member's bill, under which officials would face tough penalties for breaches. Union officials who misused funds would face fines of up to $220,000 and up to five years' jail.

Mr Tehan said that if the advocates of reform were to bring about the next stage of much-needed workplace changes, which were as necessary as when the HR Nicholls Society was founded in 1986, ''we are going to have to be much smarter in how we prosecute the case''.

The government had talked about improving productivity and reducing social disadvantage, and these were tests by which its performance on industrial relations should be judged, he said. What was happening to productivity and long-term and youth unemployment was bearing out predictions about the problems of the Labor industrial relations system.

''In my view, a decent and genuine review into the Fair Work Act and a judicial inquiry into union governance should provide the circuit-breaker to force a new political breakout,'' he told the society function.